A novel strong duality-based reformulation for trilevel infrastructure models in energy systems development

References

• Bard, J. F. (1983). An algorithm for solving the general bilevel programming problem. Mathematics of Operations Research, 8(2), 260–272. https://doi.org/10.1287/moor.8.2.260
   Web of Science ®Google Scholar
• Bard, J. F. (1991). Some properties of the bilevel programming problem. Journal of Optimization Theory and Applications, 68(2), 371–378. https://doi.org/10.1007/BF00941574
   Web of Science ®Google Scholar
• Bard, J. F., & Moore, J. T. (1990). A branch and bound algorithm for the bilevel programming problem. SIAM Journal on Scientific and Statistical Computing, 11(2), 281–292. https://doi.org/10.1137/0911017
   Web of Science ®Google Scholar
• Baringo, L., & Conejo, A. J. (2012). Transmission and wind power investment. IEEE Transactions on Power Systems, 27(2), 885–893. https://doi.org/10.1109/TPWRS.2011.2170441
   Web of Science ®Google Scholar
• Bazaraa, M. S., Sherali, H. D., & Shetty, C. M. (2013). Nonlinear programming: Theory and algorithms. John Wiley & Sons.
   Google Scholar
• Beale, E. M. L., & Tomlin, J. A. (1970). Special facilities in a general mathematical programming system for non-convex problems using ordered sets of variables. Operational Research, 69(99), 447–454.
   Google Scholar
• Belyak, N., Gabriel, S. A., Khabarov, N., & Oliveira, F. (2023). Optimal transmission expansion planning in the context of renewable energy integration policies. https://doi.org/10.1016/j.jclepro.2024.141955
   Google Scholar
• Bezanson, J., Edelman, A., Karpinski, S., & Shah, V. B. (2017). Julia: A fresh approach to numerical computing. SIAM Review, 59(1), 65–98. https://doi.org/10.1137/141000671
   Web of Science ®Google Scholar
• Burr Metzler, C. (2000). Complementarity models of competitive oligopolistic electric power generation markets. [Doctoral dissertation, The Johns Hopkins University]. https://cats.informa.com/PTS/login.do https://www.proquest.com/openview/23325a82a09fd6418e0f13c0164e2dd6/1
   Google Scholar
• Camacho-Vallejo, J.-F., Corpus, C., & Villegas, J. G. (2023). Metaheuristics for bilevel optimization: A comprehensive review. Computers & Operations Research, 161, 106410. https://doi.org/10.1016/j.cor.2023.106410
   Web of Science ®Google Scholar
• Cottle, R. W., Pang, J.-S., & Stone, R. E. (2009). The linear complementarity problem. Society for Industrial and Applied Mathematics.
   Google Scholar
• Dempe, S., & Zemkoho, A. (Editors). (2020). Bilevel optimization. In: Panos M. Pardalos, My T. Thai (Series Editors), University of Florida. Springer optimization and its applications (Vol.161). Springer. Pages 3–26.
   Google Scholar
• Dorn, W. S. (1960). Duality in quadratic programming. Quarterly of Applied Mathematics, 18(2), 155–162. https://doi.org/10.1090/qam/112751
   Google Scholar
• Dunning, I., Huchette, J., & Lubin, M. (2017). JuMP: A modeling language for mathematical optimization. SIAM Review, 59(2), 295–320. https://doi.org/10.1137/15M1020575
   Web of Science ®Google Scholar
• Dvorkin, Y., Fernandez-Blanco, R., Wang, Y., Xu, B., Kirschen, D. S., Pandzic, H., Watson, J.-P., & Silva-Monroy, C. A. (2018). Co-planning of investments in transmission and merchant energy storage. IEEE Transactions on Power Systems, 33(1), 245–256. https://doi.org/10.1109/TPWRS.2017.2705187
   Web of Science ®Google Scholar
• Facchinei, F., & Kanzow, C. (2010). Generalized Nash equilibrium problems. Annals of Operations Research, 175(1), 177–211. https://doi.org/10.1007/s10479-009-0653-x
   Web of Science ®Google Scholar
• Fischetti, M., Ljubić, I., Monaci, M., & Sinnl, M. (2018). On the use of intersection cuts for bilevel optimization. Mathematical Programming, 172(1–2), 77–103. https://doi.org/10.1007/s10107-017-1189-5
   Web of Science ®Google Scholar
• Gabriel, S. A., Conejo, A. J., Fuller, J. D., Hobbs, B. F., & Ruiz, C. (2012). Complementarity modeling in energy markets. Springer Science & Business Media.
   Google Scholar
• Gabriel, S. A., Leal, M., & Schmidt, M. (2022). On linear bilevel optimization problems with complementarity-constrained lower levels. Journal of the Operational Research Society, 73(12), 2706–2716. https://doi.org/10.1080/01605682.2021.2015254
   Web of Science ®Google Scholar
• Gao, S., & Liu, N. (2021). Improving the resilience of port–hinterland container logistics transportation systems: A bi-level programming approach. Sustainability, 14(1), 180. https://doi.org/10.3390/su14010180
   Web of Science ®Google Scholar
• Gu, Y., Cai, X., Han, D., & Wang, D. Z. (2019). A tri-level optimization model for a private road competition problem with traffic equilibrium constraints. European Journal of Operational Research, 273(1), 190–197. https://doi.org/10.1016/j.ejor.2018.07.041
   Web of Science ®Google Scholar
• Gurobi Optimization, LLC. (2022). Gurobi Optimizer Reference Manual. https://www.gurobi.com
   Google Scholar
• Hájek, M., Zimmermannová, J., Helman, K., & Rozenský, L. (2019). Analysis of carbon tax efficiency in energy industries of selected EU countries. Energy Policy, 134, 110955. https://doi.org/10.1016/j.enpol.2019.110955
   Web of Science ®Google Scholar
• Hirth, L., Mühlenpfordt, J., & Bulkeley, M. (2018). The ENTSO-E transparency platform–A review of Europe’s most ambitious electricity data platform. Applied Energy, 225, 1054–1067. https://doi.org/10.1016/j.apenergy.2018.04.048
   Web of Science ®Google Scholar
• Hobbs, B. F. (2001). Linear complementarity models of Nash-Cournot competition in bilateral and POOLCO power markets. IEEE Transactions on Power Systems, 16(2), 194–202. https://doi.org/10.1109/59.918286
   Web of Science ®Google Scholar
• Huppmann, D., & Egerer, J. (2015). National-strategic investment in European power transmission capacity. European Journal of Operational Research, 247(1), 191–203. https://doi.org/10.1016/j.ejor.2015.05.056
   Web of Science ®Google Scholar
• Ilic, M., Galiana, F., & Fink, L. (1998). Power systems restructuring: Engineering and economics. Kluwer Academic Publishers.
   Google Scholar
• IRENA (2023). Renewable capacity statistics 2023. International Renewable Energy Agency.
   Google Scholar
• Jin, S., & Ryan, S. M. (2014). A tri-level model of centralized transmission and decentralized generation expansion planning for an electricity market—Part I. IEEE Transactions on Power Systems, 29(1), 132–141. https://doi.org/10.1109/TPWRS.2013.2280085
   Google Scholar
• Karush, W. (1939). Minima of functions of several variables with inequalities as side conditions [Master’s thesis, University of Chicago].
   Google Scholar
• Keles, D., Dehler-Holland, J., Densing, M., Panos, E., & Hack, F. (2020). Cross-border effects in interconnected electricity markets-an analysis of the Swiss electricity prices. Energy Economics, 90, 104802. https://doi.org/10.1016/j.eneco.2020.104802
   Web of Science ®Google Scholar
• Kieffer, E., Danoy, G., Brust, M. R., Bouvry, P., & Nagih, A. (2020). Tackling large-scale and combinatorial bi-level problems with a genetic programming hyper-heuristic. IEEE Transactions on Evolutionary Computation, 24(1), 44–56. https://doi.org/10.1109/TEVC.2019.2906581
   Web of Science ®Google Scholar
• Kleinert, T., Labbé, M., Ljubić, I., & Schmidt, M. (2021). A survey on mixed-integer programming techniques in bilevel optimization. EURO Journal on Computational Optimization, 9, 100007. https://doi.org/10.1016/j.ejco.2021.100007
   Web of Science ®Google Scholar
• Köppl, A., & Schratzenstaller, M. (2023). Carbon taxation: A review of the empirical literature. Journal of Economic Surveys, 37(4), 1353–1388. https://doi.org/10.1111/joes.12531
   Web of Science ®Google Scholar
• Kuhn, H. W., & Tucker, A. W. (1951). Nonlinear programming. Berkeley Symposium on Mathematical Statistics and Probability, 1951, 481–492.
   Google Scholar
• Leyffer, S., Menickelly, M., Munson, T., Vanaret, C., & Wild, S. M. (2020). A survey of nonlinear robust optimization. Information Systems and Operational Research, 58(2), 342–373. https://doi.org/10.1080/03155986.2020.1730676
   Web of Science ®Google Scholar
• Nahmmacher, P., Schmid, E., Knopf, B. (2014). Documentation of LIMES-EU - A long-term electricity system model for Europe. Retrieved February 22, 2024, from https://www.pik-potsdam.de/en/institute/departments/transformation-pathways/models/limes/DocumentationLIMESEU_2014.pdf
   Google Scholar
• Pineda, S., Bylling, H., & Morales, J. (2018). Efficiently solving linear bilevel programming problems using off-the-shelf optimization software. Optimization and Engineering, 19(1), 187–211. https://doi.org/10.1007/s11081-017-9369-y
   Web of Science ®Google Scholar
• Poncelet, K., Hoschle, H., Delarue, E., Virag, A., & Drhaeseleer, W. (2017). Selecting representative days for capturing the implications of integrating intermittent renewables in generation expansion planning problems. IEEE Transactions on Power Systems, 32(3), 1936–1948. https://doi.org/10.1109/TPWRS.2016.2596803
   Web of Science ®Google Scholar
• Ribó-Pérez, D., Van der Weijde, A. H., & Álvarez-Bel, C. (2019). Effects of self-generation in imperfectly competitive electricity markets: The case of Spain. Energy Policy, 133, 110920. https://doi.org/10.1016/j.enpol.2019.110920
   Web of Science ®Google Scholar
• Ruiz, C., Conejo, A. J., & Smeers, Y. (2012). Equilibria in an oligopolistic electricity pool with stepwise offer curves. IEEE Transactions on Power Systems, 27(2), 752–761. https://doi.org/10.1109/TPWRS.2011.2170439
   Web of Science ®Google Scholar
• Santana, A., & Dey, S. S. (2020). The convex hull of a quadratic constraint over a polytope. SIAM Journal on Optimization, 30(4), 2983–2997. https://doi.org/10.1137/19M1277333
   Web of Science ®Google Scholar
• Sauma, E. E., & Oren, S. S. (2007). Economic criteria for planning transmission investment in restructured electricity markets. IEEE Transactions on Power Systems, 22(4), 1394–1405. https://doi.org/10.1109/TPWRS.2007.907149
   Web of Science ®Google Scholar
• Siddiqui, S., & Gabriel, S. A. (2013). An SOS1-based approach for solving MPECs with a natural gas market application. Networks and Spatial Economics, 13(2), 205–227. https://doi.org/10.1007/s11067-012-9178-y
   Web of Science ®Google Scholar
• Sinha, A., Malo, P., & Deb, K. (2018). A review on bilevel optimization: From classical to evolutionary approaches and applications. IEEE Transactions on Evolutionary Computation, 22(2), 276–295. https://doi.org/10.1109/TEVC.2017.2712906
   Web of Science ®Google Scholar
• Slater, M. (1950). Lagrange multipliers revisited. Cowles Foundation Discussion Papers, 304.
   Google Scholar
• Still, G. (2002). Linear bilevel problems: Genericity results and an efficient method for computing local minima. Mathematical Methods of Operations Research, 55(3), 383–400. https://doi.org/10.1007/s001860200189
   Web of Science ®Google Scholar
• Ye, J. J., & Zhu, D. (1995). Optimality conditions for bilevel programming problems. Optimization, 33(1), 9–27. https://doi.org/10.1080/02331939508844060
   Google Scholar
• Young, D. (2020). US-REGEN model documentation. Retrieved February 22, 2024, from https://www.epri.com/research/products/3002016601
   Google Scholar